Question: Simplify to lowest terms. $\dfrac{48}{120}$
Answer: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 48 and 120? $48 = 2\cdot2\cdot2\cdot2\cdot3$ $120 = 2\cdot2\cdot2\cdot3\cdot5$ $\mbox{GCD}(48, 120) = 2\cdot2\cdot2\cdot3 = 24$ $\dfrac{48}{120} = \dfrac{2 \cdot 24}{ 5\cdot 24}$ $\hphantom{\dfrac{48}{120}} = \dfrac{2}{5} \cdot \dfrac{24}{24}$ $\hphantom{\dfrac{48}{120}} = \dfrac{2}{5} \cdot 1$ $\hphantom{\dfrac{48}{120}} = \dfrac{2}{5}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{48}{120}= \dfrac{2\cdot24}{2\cdot60}= \dfrac{2\cdot 2\cdot12}{2\cdot 2\cdot30}= \dfrac{2\cdot 2\cdot 2\cdot6}{2\cdot 2\cdot 2\cdot15}= \dfrac{2\cdot 2\cdot 2\cdot 3\cdot2}{2\cdot 2\cdot 2\cdot 3\cdot5}= \dfrac{2}{5}$